EEF 210E - Differential Equations

Course Objectives

1 Introduction. First Order Differential Equations (Basic Concepts, A Simple DE Example,
Clasification of DEs)
I - II
2 First Order Differential Equations (Linear Eqns, Separable Eqns, Existence and Uniqueness
Thm)
II-III
3 First Order Differential Equations (Exact Eqns, Homogeneous Eqns, Riccati Eqn) II - III
4 Second Order Differential Equations (Constant Coefficient, Homogeneous,Linear DE, Basic
Theorems and the Wronskian, Complex Roots of the Characteristic Eqn)
III - IV
5
Second Order Differential Equations (Repeated Roots of the Characteristic Eqn, Reduction of
Order, Nonhomogeneous Eqns, Method of Undetermined Coefficients, Variation of
Parameters)
IV
6
Second Order Differential Equations (Mechanical and Electrical Vibrations, Forced
Vibrations), Higher Order Differential Equations (General Theory of nth Order Linear
Equations)
III - IV
7 Higher Order Differential Equations (Homogeneous Eqns with Constant Coefficients, Method
of Undetermined Coefficients, Method of Variation of Parameters)
IV
8 The Laplace Transform (Definition of Laplace Transform, Initial Value Problems, Step
Functions)
V
9 The Laplace Transform (DE with Discontinuous Forcing Functions, Impulse Function,
Convolution Integral)
V
10 Systems of First Order Linear Equations (Introduction, Basic Theory of Systems of
First Order Linear Equations)
VI
11 Systems of First Order Linear Equations (Homogeneous Linear Systems with Constant
Coefficients, Complex Eigenvalues, Fundamental Matrices)
VI
12 Systems of First Order Linear Equations (Repeated Eigenvalues, Nonhomogeneous Linear
Systems)
VI
13 Series Solutions of Second Order Linear Equations (Series Solutions Near an Ordinary Point,
Euler Equations, Regular Singular Points)
VII
14 Series Solutions of Second Order Linear Equations (Series Solutions Near a Regular Singular
Point)
VII

Course Description

1 Introduction. First Order Differential Equations (Basic Concepts, A Simple DE Example,
Clasification of DEs)
I - II
2 First Order Differential Equations (Linear Eqns, Separable Eqns, Existence and Uniqueness
Thm)
II-III
3 First Order Differential Equations (Exact Eqns, Homogeneous Eqns, Riccati Eqn) II - III
4 Second Order Differential Equations (Constant Coefficient, Homogeneous,Linear DE, Basic
Theorems and the Wronskian, Complex Roots of the Characteristic Eqn)
III - IV
5
Second Order Differential Equations (Repeated Roots of the Characteristic Eqn, Reduction of
Order, Nonhomogeneous Eqns, Method of Undetermined Coefficients, Variation of
Parameters)
IV
6
Second Order Differential Equations (Mechanical and Electrical Vibrations, Forced
Vibrations), Higher Order Differential Equations (General Theory of nth Order Linear
Equations)
III - IV
7 Higher Order Differential Equations (Homogeneous Eqns with Constant Coefficients, Method
of Undetermined Coefficients, Method of Variation of Parameters)
IV
8 The Laplace Transform (Definition of Laplace Transform, Initial Value Problems, Step
Functions)
V
9 The Laplace Transform (DE with Discontinuous Forcing Functions, Impulse Function,
Convolution Integral)
V
10 Systems of First Order Linear Equations (Introduction, Basic Theory of Systems of
First Order Linear Equations)
VI
11 Systems of First Order Linear Equations (Homogeneous Linear Systems with Constant
Coefficients, Complex Eigenvalues, Fundamental Matrices)
VI
12 Systems of First Order Linear Equations (Repeated Eigenvalues, Nonhomogeneous Linear
Systems)
VI
13 Series Solutions of Second Order Linear Equations (Series Solutions Near an Ordinary Point,
Euler Equations, Regular Singular Points)
VII
14 Series Solutions of Second Order Linear Equations (Series Solutions Near a Regular Singular
Point)
VII